हिंदी

If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.

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प्रश्न

If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.

अति संक्षिप्त उत्तर
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उत्तर

The relation is symmetric and transitive but not reflexive.

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2025-2026 (March) Specimen Paper

संबंधित प्रश्न

Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is ______.


Test whether the following relation R1 is  (i) reflexive (ii) symmetric and (iii) transitive :

R1 on Q0 defined by (a, b) ∈ R1 ⇔ = 1/b.


Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.


Show that the relation R on the set A = {x ∈ Z ; 0 ≤ x ≤ 12}, given by R = {(a, b) : a = b}, is an equivalence relation. Find the set of all elements related to 1.


Show that the relation R, defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have the same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right-angled triangle T with sides 3, 4 and 5?


A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(xy) : y is one half of xxy ∈ A} is a relation on A, then write R as a set of ordered pairs.


The relation 'R' in N × N such that
(a, b) R (c, d) ⇔ a + d = b + c is ______________ .


Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ________________ .


If R is the largest equivalence relation on a set A and S is any relation on A, then _____________ .


If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y ⇔ y = 3 x, then R = _____________ .


Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) is ______.


Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∩ C).


In the set of natural numbers N, define a relation R as follows: ∀ n, m ∈ N, nRm if on division by 5 each of the integers n and m leaves the remainder less than 5, i.e. one of the numbers 0, 1, 2, 3 and 4. Show that R is equivalence relation. Also, obtain the pairwise disjoint subsets determined by R


Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = ______


If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.


The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is


A relation in a set 'A' is known as empty relation:-


Read the following passage:

An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project.
Let B = {b1, b2, b3} and G = {g1, g2}, where B represents the set of Boys selected and G the set of Girls selected for the final race.

Based on the above information, answer the following questions:

  1. How many relations are possible from B to G? (1)
  2. Among all the possible relations from B to G, how many functions can be formed from B to G? (1)
  3. Let R : B `rightarrow` B be defined by R = {(x, y) : x and y are students of the same sex}. Check if R is an equivalence relation. (2)
    OR
    A function f : B `rightarrow` G be defined by f = {(b1, g1), (b2, g2), (b3, g1)}. Check if f is bijective. Justify your answer. (2)

Statement 1: The intersection of two equivalence relations is always an equivalence relation.

Statement 2: The Union of two equivalence relations is always an equivalence relation.

Which one of the following is correct?


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